Some revisited results about composition operators on Hardy spaces
We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨ; construction of a surjective symbol whose composition operator is compact on HΨ a...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/46376 |
| Acceso en línea: | http://hdl.handle.net/11441/46376 https://doi.org/10.4171/RMI/666 |
| Access Level: | acceso abierto |
| Palabra clave: | Blaschke product Carleson function Carleson measure Composition operator Hardy-Orlicz space Nevanlinna counting function Schatten classes |
| Sumario: | We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨ; construction of a surjective symbol whose composition operator is compact on HΨ and, moreover, is in all the Schatten classes Sp(H2), p > 0. On the other hand, we revisit the classical case of composition operators on H2, giving first a new, and simplier, characterization of closed range composition operators, and then showing directly the equivalence of the two characterizations of membership in the Schatten classes of Luecking and Luecking and Zhu. |
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